Question

A hint please? Please help!!
(sinx+sin3x)/(2sin2x) = cosx

Answer 1

you know the sin C+sin D formula ?

Answer 2

um i know the formulas sin(2x) = 2 sinxcosx and I know I have to split the Sin(3x) into sin(2x+x) and cos(2x)= 2cos^2x-1

so far I've got sinx + 2sinxcosx(cosx) + 2cos^2x-1(sinx) I don't know if that's right

Answer 3

try this :
\(\sin C +\sin D = 2 \sin[ (C +D)/2] \cos [(C -D)/2]\)

Answer 4

lol Yea i saw that on Youtube but i'm just hesitant to use that because my professor didn't teach that formula haha

Answer 5

there are multiple ways, this one is short...but if you want to try your method, we can do that.... ?

Answer 6

yes please! i'm just not sure if what I'm doing is correct.

my first step was

sinx + sin(2x +x)/ 2sin2x

then the top would be

sinx + sin(2x)cos(x) + cos(2x)sinx

then cos(2x) would change to 2cos^2x-1

sooo it would be sinx + sin(2x)cos(x) + 2cos^2x-1(sinx)

am i on the right track?

Answer 7

don't miss the brackets! or else next step will become incorrect..

sinx + sin(2x)cos(x) + (2cos^2x-1)(sinx)

Answer 8

open the brackets and notice anything getting cancelled ?

Answer 9

urmm no haha i'm not sure O.o

Answer 10

open up the brackets! you can do that, right ?

Answer 11

do the sin's cancel out?

Answer 12

yes!

Answer 13

then ?

Answer 14

we are very close to the answer :)

Answer 15

would i be left with sin(2x)cosx + 2cos^2sinx ?

Answer 16

ofcourse

factor out cos x from that ans see the magic ;)

Answer 17

cos(sin(2x) + 2cosxsinx) ?

Answer 18

and 2 sin x cos x = .. ?

Answer 19

sin2x!

Answer 20

i think you can finish :)

Answer 21

cos(2sin(2x)/(2sin(2x) = cos!!!!!!! YASSSS OMGGG!!!! :-) XD XD XD :-)